URGENT: Can someone check my working on these Diff Eqs. Hi I have a maths exam tomorrow, and want to make sure Im doing the right thing, please bare in mind i study physics, and am not used to some of the techniques that are used in pure maths, so if the person can help using the methods i am using, would be much appreciated. Question 1) Solve this first order differential equation dy/dx = x^3/y subject to the boundary condition that y(x=0)=1 ok so what I do is rearrange to get: 1/y dy = x^3 dx and then integrate both sides with respect to their variable to get ln y = 1/4 x^4 + c so then i remove the ln: y = e^(1/4 x^4 + c) SO now im a little bit confused with the boundary conditions, am I right in saying that when x = 0 , y = 1?? if that is true then am I right in saying that the constant of integration must be 0 (as e^0 = 1), so the answer is: y = e ^ (1/4 x^4) ?? Question 2) Solve the 2nd order differential equation: d^2y/dx^2 - 4dy/dx = 0 (no boundary conditions this time) ok so here i used the substitution U = dy/dx and get dU/dx - 4U = 0 and rearrange to get: 1/U dU = 4 dx and similarly to above integrate both sides ln U = 4x + c1 rearrange: dy/dx = U = e ^ (4x +c1) ok, so now im slightly confused, do I ignore the constant becasue there are no bc's in this question???? If that is right, then I just integrate again to get: y = 4 e^(4x) + C is that correct??